The Critical Potentials of Molecular Hydrogen

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trons to about 1/2, and 11.78 takes away practically the other half. It may be that the number of electrons, whose speed is higher than the lower resonance potential 11.57, is less than 1/2. However, it is certain that there is still a considerable number of electrons with speeds between 11.57 and 11.77 volts. The fact that no continuous spectrum appears suggests that the terms of the triplet system lie about 0.1 volt higher relative to the singlet system than the values given by Birge.3 As no intersystem combinations are known the value of the triplet terms relative to 11S are calculated by the extrapolations (m = co) of the Ritz formula for the series 21S-m'P and 23S-m3P. The extrapolation of the later series, where bands for m = 3, 4, 5, 6, 7 and 8 are known, is probably very accurate. The extrapolation of the singlet system, however, is less certain as only bands for m = 3 and 4, and a few lines probably belonging to m = 5, are known. In conclusion we wish to express our thanks to Prof. E. U. Condon for his very helpful suggestions. * NATIONAL RsuARc FJLLOW. 1 J. Frank u. P. Jordan, Anregung von Quantenspruengen durch Stoesse, p. 261; J. Kaplan, Proc. Nat. Acad. Sci., 13, 760, 1927. 2 W. Heitler and F. London, Zeits. Physik, 44, 455, 1927; Y. Sugiura, Ibid., 45, 484, 1927. 8 R. T. Birge, Proc. Nat. Acad. Sci., 14, 12, 1928. ' E. U. Condon, Physic. Rev., 28, 1182, 1926; Proc. Nat. Acad. Sci., 13, 462, 1927. A detailed discussion of the wave mechanical interpretations of this theory as used here is to be given soon in the Physical Review. For the opportunity of seeing the manuscript and conversations on the subject of this paper, we wish to express our thanks to Prof. Condon. 6J. Franck, Trans. Far. Soc., 21, part-3, 1925. 6 J. Stark, M. Goercke u. M. Arndt, Ann. Physik, 54, 69, 1917. 7 W. Witmer, Physic. Rev., 28, 1223, 1926.

THE CRITICAL POTENTIALS OF MOLECULAR HYDROGEN By E. U. CONDON AND H. D. SMYTH P.ALMZR PHYSiCAL LABORATORY, PIINCIITON UNIVSRSITY

Communicated September 24, 1928

Out of a number of experiments in recent years on the impact.of electrons with hydrogen molecules, there come certain results which at first sight appear discordant. On the one hand the experiments on ionization show that an electron, when it ionizes a hydrogen molecule, does so without causing dissociation. That is, the production of atomic ions as the primary result of impact of moderate speed electrons with hydrogen molecules is a process which occurs rarely if at all. On the other hand,

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dissociation into uncharged atoms by electrons with velocities both below and above the ionizing potential, does occur frequently. There is therefore an apparent inconsistency, but the writers believe it is explained by theoretical considerations similar to those advanced by Winans and Stueckelberg' in the preceding paper. In fact almost all the critical potential data on hydrogen now seem to fit in the theoretical scheme. However, before presenting the theory, a more precise summary of the experimental results will be given. Suppose we present the experimental observations as a function of the speed of the impacting electrons. If diatomic hydrogen be bombarded by electrons of any speed below eleven volts the electrons lose a small indeterminate amount of energy; that is, the collisions are not perfectly elastic as in the rare gases, but are very nearly so. No effect of radiation or dissociation is observed. As the speed of the electrons is increased up to twelve volts several effects2 are observed, first inelastic impact,3 second radiation photoelectrically effective,4 third the production of atomic hydrogen (or at least of some form of hydrogen that "cleans up" and is chemically active4'5). The exact critical potentials where these processes begin to occur are not very precisely determined but are all in the neighborhood of 11.5 volts. Now, if the speed of the electrons is further increased the experimental evidence is less definite. Apparently radiation becomes more intense, possibly with discontinuities corresponding to higher critical potentials. In particular a number of investigators report an increase in radiation at about 12.8 volts. As to the production of atoms, that also appears to increase. Thus, Glockler, Baxter and Dalton5 state that the effectiveness of the impacting electrons increases rapidly between 11.4 volts and the molecular ionizing potential above which the change is slow. Experiments on inelastic impact give no definite results in this region. When the electrons reach a speed of 13.5 volts, the ionizing potential of atomic hydrogen, weak ionization is always observed, indicating that there is always some atomic hydrogen present. In the past this has been explained by dissociation due to the hot filament. Somewhat above this voltage but before the molecular ionization potential, are a group of radiating potentials observed by Olsen and Glockler but in no other experiments. Then at about 15.9 volts strong ionization sets in, which has been shown to be ionization without dissociation. Furthermore, no evidence has been found at this or any higher voltage of the formation of atomic ions from molecules as the immediate result of an electron impact. However, such a process may occur if of very small probability, since it might be masked by the large number of atomic ions formed by secondary dissociation of the molecular ions. This latter process occurs only if the molecular ions

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have acquired a certain minimum kinetic energy before they make collisions. (See Dorsch and Kallmann, Zs. Phys., 44, p. 543, 1927.) As the speed of the impacting electrons is still further increased no new processes are observed by the positive ray or "clean-up" methods. Some experimenters have observed additional ionization setting in at about thirty volts. Of more importance, however, are the results of Franck and Blackett, who showed that the emission of Balmer lines was a primary result of impact of thirty volt or higher speed electrons. In other words, they showed dissociation may occur with excitation of one (or perhaps both) atoms. We may summarize the principal results in tabular form as given below. MINIMUM SNSRGY

PROCSSS

(a) (b) (c) (d) (e)

H2

H+H Radiation produced More radiation H2 > H2+ + e H2 > H+ + H + e H2 - H' + H(or H')

RSQUIRSD

RSMARKS

11.5 12.8 15.9

Not very definite The usual ionization Does not occur

30

It should be pointed out that we have little evidence as to the relative probabilities of these processes at different voltages, though from the small number of atomic ions observed at low pressures we may infer that (a) is improbable compared to (b) at potentials above 15.9. In order to interpret these phenomena in terms of energy levels and potential energy curves we will need not only those given in the previous paper but also the potential energy curve for the normal state of the hydrogen molecular ion. This has been calculated by Burrau.6 In the figure a curve drawn from his data is given. To it have been added a curve for the 21S from band spectra data and the curves given by Winans and Stueckelberg for the 1'S and 23S states. Consider the possible effect of an electron impact on an H2 molecule. If the electron has less than 11 volts the only possible transition it may cause is to the 13S state. But applying the Franck-Condon principle we see that the probability of such a transition will be small except for those nuclear separations where the 1'S curve nearly coincides with that for the 23S term. In other words we might expect a little but only a little atomic hydrogen to be produced below eleven volts since the 13S state is unstable. Slightly above eleven volts the excitation to the 21S state becomes possible. Although the nuclear binding in this state is considerably weaker than in the normal state and the curve suggests the possibility of dissociation on excitation to this state, the intensity, distribution in the absorption bands indicates that this is not usually the case.7 Return from this state to the normal would, of course, produce radiation that would be photoelectrically effective.

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IPROC. N. A. S.

Electrons of somewhat greater speed might do any of three things, (1) excite directly to the 13S state producing hydrogen atoms with big kinetic energy, (2) excite to the 21S state producing radiation, (3) excite to the 23S state which would then revert to the 13S state giving off the continuous spectrum and producing atomic hydrogen simultaneously. The writers believe that some or all of these three processes occur in the various experiments which find a critical potential at about 11.5 both for the production of radiation and of atomic hydrogen. If the speed of the electrons be still further increased the possibilities become more and more numerous. We may suggest the correlation of

>/2O,OOvM

Rin cm*/o8° The curves in the above figure represent the potential energy as a function of nuclear separation for five different electronic states of the hydrogen molecule. The values given at the right for the heats of dissociation are obtained from band spectra for 11S and 21S states and from Burrau's paper for the ion. They indicate the heights which the curves would approach if extended to the righlt.

the 12.8 radiating potential with the "C" level but the uncertainties of both theory and experiments make further correlations futile. Two points remain to be mentioned for this region of velocities. First, we may expect more and more atomic hydrogenl to be produced by excitationl to higher triplet levels and reversion to the 13S. Second, the presence of this atomic hydrogen probably explains the atomic critical potentials which are so often observed. Finally, suppose the electrons have sufficient velocity to ionize the molecule, that is to change it from the lowest to the topmost curve in our figure. If we compare the shapes of the two curves and positions of

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their minima, we see at once that the most probable transitions are going to give nuclear separations which will not result in dissociation. This is in perfect accord with experiment. Until we know more of the excited states of the H2+ ion we cannot proceed with explanations of the effects that still faster electrons may produce. 1 Winans and Stueckelberg, these PROCUZDINGS, 14, 867, 1928. 2 We are assuming the weak ionization sometimes reported at about 11 volts, is due to an impurity. 8 Compton and Mohler, Critical Potentials, p. 115. 4 Hughes and Skellet, Physic. Rev., 30, pp. 11-35, 1927. 6 Glockler, Baxter and Dalton, J. Am. Chem. Soc., 49, pp. 58-65, 1927. 6 Burrau, Kgl. Danske Vid. Selskal. Math-fys. Med., 7, 14, 1927. 7 Hopfield, Physic. Rev., 31, p. 918, 1928.

THE STRUCTURE OF THE COMPTON SHIFTED LINE BY Jzssz W. M. DUMOND NORMAN BRIDGE LABORATORY OF PHYSICS, CALIFORNIA INSTITUTg or TsCHNO1OGY

Communicated October 13, 1928 According to Wentzel's' wave mechanical theory of modified x-ray scattering and also according to Jauncey's2 classical-quantum theory of the same effect (though not explicitly so stated by Jauncey), the modified scattered x-radiation is regarded as due to many Smekal transitions3 in each of which the initial state of the electron is a discrete negative energy level and the final state is one of the continuum of positive energy levels. In both of these theories the shifted "line" is predicted as a diffuse band, the diffuseness being due to the momenta of bound electrons in the dynamic atom model. Indeed, the natural breadth of the Compton modified line can be regarded as a Doppler broadening for x-rays scattered by moving electrons in much the same way as the temperature broadening is regarded in the case of optical spectra. The broadening of the Compton line is the most direct evidence for a dynamic atom model yet found. The structure of the line can be interpreted in such a way as to give the probability distribution of electron momenta in atoms. The breadth for circular orbits should be proportional to the effective atomic number of the scatterer. In order to determine the natural structure of the Compton modified line it is necessary to first minimize an experimental cause for the breadth of Ithe line which is ordinarily superposed upon the natural breadth so as to mask the latter. This cause is the unavoidable inhomogeneity of scattering angle. The x-radiation incident upon the scattering material